#include <algorithm>
#include <iostream>

using namespace std;

int main() {
  string pref;
  for (int i = 1; i < 111; ++i) pref += to_string(i);
  for (int tc = (cin >> tc, tc); tc--; ) {
    string s; cin >> s;
    int found = 0;
    for (int i = 0; i + s.size() < pref.size() && !found; ++i) {
      bool ok = 1;
      for (int j = 0; j < s.size(); ++j) ok &= s[j] == '?' || pref[i + j] == s[j];
      if (ok) found = i + 1;
    }
    if (found) {
      cout << found << '\n';
      continue;
    }
    __uint128_t ans = -1;
    for (int len = 3; len <= s.size() + 1; ++len)
    for (int ofs = 1; ofs <= len; ++ofs)
    for (int mod10 = 0; mod10 < 10; ++mod10)
    for (int c9 = -1; c9 < len; ++c9) if (ofs + len * (9 - mod10) < s.size() == !!~c9) {
      string first(len - 1, '?');
      first += mod10 + '0';
      for (int i = c9; i-- > 0; ) first.end()[-i - 2] = '9';
      bool ok = 1;
      for (int os = 0, on = ofs, d = 0; os < s.size() && ok; ++os, --on) {
        if (on == 0) ++d, on = len + (d + mod10 >= 10 && c9 + 1 == len);
        if (s[os] == '?') continue;
        char cs = s[os];
        if (on == 1) cs = (s[os] - '0' + 10 - d) % 10 + '0';
        else if (d + mod10 >= 10 && on <= c9 + 2) cs = (s[os] - '0' + 9) % 10 + '0';
        if (on > len) ok &= cs == '0';
        else if (first.end()[-on] == '?') first.end()[-on] = cs;
        else if (first.end()[-on] != cs) ok = 0;
      }
      if (~c9) ok &= c9 == len - 1 || first.end()[-c9 - 2] != '9';
      ok &= first[0] != '0';
      if (!ok) continue;
      if (first[0] == '?') first[0] = '1';
      for (__uint128_t l = 1; l < len; ++l) if (first[l] == '?') first[l] = '0';
      __uint128_t cans = 0;
      for (__uint128_t l = 1, p = 9; l < len; ++l) cans += p * l, p *= 10;
      for (__uint128_t l = 0, p = 1; l < len; ++l) cans += p * (first.end()[-l - 1] - '0' - (l == len - 1)) * len, p *= 10;
      cans += len - ofs + 1;
      ans = min(ans, cans);
    }
    cout << int(ans % 998244353) << '\n';
  }
}